The colonization of the east coast have very little to do with 'Britain', i.e. the British government. Yes, there was some transportation of criminals for a while, but mostly the settlements were groups of people (with government approval or without) doing the settlement. Some were self funded (i.e. by the settlers), some were encouraged (with various incentives) by the Lord Proprietor of the colony who found colonists and shipped them over. Transportation and communication were difficult just the distance of the Atlantic. Going all the way around the Horn? ouch.
That model just won't work for California. No one is going to be interested in that long a voyage with that chance of death, when they could go to existing colonies.
Your best bet, IMO, is to get about a single ship load of people out there, with the intent of getting more later, but few ever join them.
The distance is great enough that commerce is surely impossible - unless and until they discover the gold.
On the other hand, the distance to Mexico is a lot less, and some Spanish viceroy is likely to send a troop of soldiers north to reassert Spanish control.
Which would mean the 'British' colony soon becomes a Spanish one.
Again, where do the colonists get their metal from? Iron they can likely find enough of for at least tools, but copper? tin? lead?
You'd need that original ship to be loaded with 100% farmers, 10% miners, 10% smiths, 10% engineers, 50% soldiers.... (plus all the women and children). Unless you're willing for the colony to lose all their guns and things like cutlery in a generation. Oh, and remember that if you want to have this shipload of remarkable multitalented prodigies to arrive, you probably have to fill three ships with them so a single one makes it all the way. Given the distance and dangers.